Gauge-independent approach to inflation in quadratic gravity

TL;DR

This paper develops a gauge-independent method to analyze scalar perturbations in quadratic gravity, revealing that apparent instabilities in some gauges are gauge artefacts, thus ensuring consistent physical predictions across frames.

Contribution

The authors introduce a gauge-invariant framework for studying cosmological perturbations in quadratic gravity, clarifying the physical nature of instabilities and frame transformations.

Findings

The Newtonian gauge shows an apparent exponential instability.

Gauge-invariant variables remain well-behaved, indicating no physical instability.

The gauge artefact nature of the instability is confirmed across multiple gauges.

Abstract

We investigate the scalar sector of linear cosmological perturbations in quadratic gravity. Working in the Einstein frame, we derive the equations of motion in a gauge-independent manner and express them in terms of three sets of gauge-invariant variables. This approach allows us to distinguish genuine physical effects from gauge artefacts, which is particularly relevant for assessing the stability of perturbations in this theory. In the superhorizon limit, we obtain the leading-order behaviour of the relevant gauge-invariant variables and analyse the perturbations in several commonly used gauges. We find that the Newtonian gauge exhibits an apparent instability, characterised by the exponential growth of the metric perturbations. However, this growth is non-generic and gauge-dependent; in the other gauges analysed in this work, the perturbations remain well behaved within the perturbative regime. Physical observables can thus be consistently computed, and the apparent instability is identified as a gauge artefact rather than a pathology of the theory. Our analysis also demonstrates how the evolution behaviour of a gauge-invariant variable changes under the frame transformation and clarifies the relation between results obtained in the Jordan and Einstein frames.